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THE TRANSPORTATION OF GASES
171
The proper intercooler pressures for three-stage compression are: First intercooler, p = \^pizpzj second intercooler, p = v/pi^22 The minimum work done in compressing air is given by
(n-l
horsepower = 2 X 00 Ar>A — ^rpi^r   ( — I 2n   ~ 1    f°r two-stage compressors, ddjUUU n — 1         L \Pi/              J
(n — 1
and horsepower = 3 X -OQ AA~ — ^— vpii>r    ( — )  3n — 1   for three-stage compressors. oojlHJU n — 1         l_ \pij           J
_
With perfect intercooling the volumes of the cylinders should be inversely as the pressures of the air admitted to them.
Professor Lucke (" Engineering Thermodynamics") gives a numbei solving graphically many of the problems of air compression, of whic'
Abs. Pressure, Ib.per sq.'m. of Air Drawn fn» 18     17   16   15L7>4-    V5    \2    H     10    9     S.    7
4'    **>    2      1     C
7:8       9
j Pressure Ratio. I
14
15
12. J; 13
j   i rci^uvc uuniv.  t            »            I     j      I            •            |
8,000 7,200  6,400 ! 5,600   4,600  4,000   #00   2,400:1,600   SOO.      0
j        Ft.-lb.percu.fr.of Air Drawn in.         j        '               |
240                  180              _   )io-                 60                 6 H.p. per 1000 cu/ft.of Air Drawn In p^rMin.
Fio. 31.—Chart for determining the work done in single-stage air compression (Lucke).
10,400:9,600
• 30Q
very convenient one for determining the work per cubic foot and the horsepower per 1,000 cu. ft. of free air compressed in a single stage to any pressure up to 15 times its initial pressure and for various kinds of compression curves from the isothermal to the adiabatic.
In Fig. 31 the diagonal lines represent various absolute pressures for the free air drawn in and the curved lines apply to various kinds of compression curves. The lower horizontal scale gives pressure ratios, work and horsepower. In using the curves follow vertically from the pressure ratio to the n curve, horizontally to the inlet pressure lino and vertically downward to the horizontal axis where the work and horsepower may be read. For example, if the compression ratio is 6, the compression curve follows the equation piVi1^ = TwV'4, and the free air is at 14.7 Ib. per square inch absolute, there will be required 4,960 ft.-lb. of work per cubic foot of free air compressed, or 152 hp. per 1,000 cu. ft. of free air per minute.
If the compression for the same pressure range (or to 88.2 Ib. per square inch absolute) had followed the isothermal compression curve it would have required 3,880 ft.-lb. of work per cubic foot, or 120 hp. per 1,000 cu. ft. per minute.
Figure 31 enables calculations to be made for work and horsepower for two- and three-stage compression, when used in connection with Fig. 31. The dotted lines represent two-stage and the full lines three-stage compression, and are marked according